Thermodynamic geometry of Kaniadakis statistics

Abstract

We consider the thermodynamic geometry of an ideal gas with particles obeying Kaniadakis statistics. We work out the thermodynamic curvature of κ-Maxwell–Boltzmann, κ-Bose and κ-Fermi gases. Curvature of thermodynamic parameters space of an ideal ordinary classical gas is zero while it is negative for κ-classical gas. Also, the thermodynamic curvature of an ideal κ-Fermi gas is negative such as ordinary fermion gas. For an ideal κ-Bose gas, two different regimes is found. In fact, we introduce a specified value of temperature; T*, where for T > T* (T < T*) the thermodynamic curvature is negative (positive) and intrinsic statistical interaction is repulsive (attractive) while for an ordinary ideal boson gas, the thermodynamic curvature is positive and the statistical interaction is attractive in full physical range. Therefore, we argue that the κ induces repulsive interaction to particles. Finally, we consider the singular points of thermodynamic curvature of κ-Bose gas and work out the condensation temperature.